Surface tension of water droplets upon homogeneous droplet nucleation in water vapor

A method has been proposed for determining interfacial free energy from the data of molecular dynamics simulation. The method is based on the thermodynamic integration procedure and is distinguished by applicability to both planar interfaces and those characterized by a high curvature. The workability of the method has been demonstrated by the example of determining the surface tension for critical nuclei of water droplets upon condensation of water vapor. The calculation has been performed at temperatures of 273–373 K and a pressure of 1 atm, thus making it possible to determine the temperature dependence of the surface tension for water droplets and compare the results obtained with experimental data and the simulation results for a “planar” vapor–liquid interface.     

Relation between homogeneous nucleation rate and supersaturation in pyrolysis of methane

Conclusions The existence of a maximum for the function: homogeneous nucleation rate of carbon vs methane pressure, was established on the basis of the theory of homogeneous nucleation from the vapors.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2416–2417, October, 1978.     

A study of sulfur homogeneous nucleation from supersaturated vapor. Determination of surface tension of sulfur nanoparticles

Homogeneous nucleation in sulfur vapor is studied in a laminar-flow chamber. Concentration and size distribution of resulting aerosol particles are measured with a diffusion spectrometer of aerosols and a PK.GTA-0,3-002 photoelectric particle counter. The crystal structure of the formed particles is studied by X-ray diffraction analysis. The rate of sulfur evaporation from a boat and the profile of a deposit on the chamber wall along the axial coordinate are determined by gravimetry. Axial and radial temperature profiles are measured using a chromel-alumel thermocouple. The vapor concentration distribution in the chamber is found and the supersaturation is calculated from the solution of the mass-transfer problem. An experimental low-laborious method is developed for the supersaturation cutoff. This method enables one to rapidly deter-mine the position of the zone in which the nucleation proceeds at the highest rate. The position of the zone of nucleation found by this method is in good agreement with the results of calculations based on experimental data and theoretical calculation of the rate of nucleation by an exact formula that has been recently derived based on the works by Kusaka and Reiss, as well as the Frenkel liquid kinetics theory. The surface tension of critical sulfur nuclei resulting from the nucleation is calculated based on this formula and experimental data on the nucleation. It is established that, in a temperature range of 312–319 K, the critical nuclei have tension surface radius R _s ～ 10.6 Å and surface tension σ = 72.5 ± 1.1 dyn/cm. The surface tension of critical sulfur nuclei in this temperature range is constant and approximately 5% higher than that of a planar surface.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

Molecular dynamics determination of the surface tension of silver-gold liquid alloys and the Tolman length of nanoalloys

Using molecular dynamics simulations, an embedded-atom model potential, and the mechanistic route, we have computed the pressure tensor and the surface tension γ of Ag-Au liquid alloys. Although the model generally underestimates γ for pure metals, calculations for a bulk planar slab exhibit nonlinear variations of γ with increasing gold concentration, which agree with experiments and can be accounted for by a perfect solution model. Calculations for various nanoscale droplets containing between 100 and 3200 atoms show a systematic decrease of γ with increasing droplet radius R. The positive Tolman length of the alloy determined from these size variations is estimated to vary slightly with gold concentration. The effects of temperature in the range 1300-1700 K are discussed.     

Statistico-probabilistic approach to taking account of the vapor depletion in the kinetics of homogeneous nucleation: a free-molecular regime of droplet growth

We propose a statistico-probabilistic approach to investigate the process of homogeneous formation of droplets in a vapor phase in the presence of an already formed and growing droplet under free-molecular regime of droplet growth after the instantaneous creation of initial vapor supersaturation. We find the probability density for the formation of a new, nearest (neighbor) droplet in the vicinity of an initially formed droplet. The mean distance between two neighboring droplets is also determined, as well as the average time lag for the formation of the nearest (neighbor) droplet; the latter quantity serves as an estimate for the duration of the nucleation stage. An estimate for the average number of droplets forming in unit volume by the end of the nucleation stage is also given. Our results are compared with the predictions of classical nucleation theory which assumes the density uniformity of a metastable phase. Where the proposed approach is applicable, there is observed qualitative agreement between the results. The underlying cause of this agreement is analyzed and the limits of applicability of the uniformity approximation are clarified.     

Gradient theory computation of the radius-dependent surface tension and nucleation rate for n-nonane clusters

The Van der Waals-Cahn-Hilliard gradient theory (GT) is applied to determine the structure and the work of formation of clusters in supersaturated n-nonane vapor. The results are analyzed as functions of the difference of pressures of the liquid phase and vapor phase in chemical equilibrium, which is a measure for the supersaturation. The surface tension as a function of pressure difference shows first a weak maximum and then decreases monotonically. The computed Tolman length is in agreement with earlier results [L. Granasy, J. Chem. Phys. 109, 9660 (1998)] obtained with a different equation of state. A method based on the Gibbs adsorption equation is developed to check the consistency of GT results (or other simulation techniques providing the work of formation and excess number of molecules), and to enable an efficient interpolation. A cluster model is devised based on the density profile of the planar phase interface. Using this model we analyze the dependency of the surface tension on the pressure difference. We find three major contributions: (i) the effect of asymmetry of the density profile resulting into a linear increase of the surface tension, (ii) the effect of finite thickness of the phase interface resulting into a negative quadratic term, and (iii) the effect of buildup of a low-density tail of the density profile, also contributing as a negative quadratic term. Contributions (i)-(iii) fully explain the dependency of the surface tension on the pressure difference, including the range relevant to nucleation experiments. Contributions (i) and (ii) can be predicted from the planar density profile. The work of formation of noncritical clusters is derived and the nucleation rate is computed. The computed nucleation rates are closer to the experimental nucleation rate results than the classical Becker-D?ring theory, and also the dependence on supersaturation is better predicted.     

Estimation of line tension and contact angle from heterogeneous nucleation experimental data

Using the classical nucleation theory corrected with line tension and experimental data of heterogeneous nucleation of n-nonane, n-propanol, and their mixture on silver particles of three different sizes, the authors were able to estimate the line tensions and the microscopic contact angles for the above mentioned systems. To do this they applied generalized Young's equation for the line tension and calculated the interfacial tensions using Li and Neumann's equation [Adv. Colloid Interface Sci. 39, 299 (1992)]. It has been found that, for both unary and binary systems, the line tension is negative and the resulting microscopic contact angle derived from experimental nucleation data is most of the time larger than the macroscopic one. This is in contrast to earlier studies where the influence of line tension has not been accounted for. The values of the three phase contact line tension obtained in this way are of the same order of magnitude as the estimations for other systems reported in literature. The line tension effect also decreases considerably the nucleation barrier.     

A study of homogeneous nucleation of ibuprofen in a flow chamber. Determination of the surface tension of critical nuclei

Homogeneous nucleation of ibuprofen vapor is studied in a nucleation flow chamber, a horizontal quartz tube equipped with an external heater. The area of the chamber where the nucleation proceeds most efficiently is determined, and the volume of this area is estimated. The temperature and supersaturation are determined and the homogeneous nucleation rate is calculated for this area. Saturation vapor pressure over liquid ibuprofen is measured in a temperature range of 353–383 K. Using an exact formula that has recently been derived for the nucleation rate based on the works by Kusaka, Reiss, as well as the Frenkel liquid-kinetics theory, surface tension and the radius of surface of tension of a critical nucleus σ= 25.9 mN/m and R _s = 1.6 nm, respectively, are calculated at 318 K. The measurement of the surface tension of an ibuprofen planar surface shows that, at 318 K, σ_∞ = 24.38 mN/m; i.e., σ is higher than σ_∞ by 6%. A critical nucleus is established as containing nearly 36 ibuprofen molecules.     

Homogeneous nucleation of water between 200 and 240 K: new wave tube data and estimation of the Tolman length

We have measured homogeneous nucleation rates of water at 200-240 K in the carrier gas helium, in the range of 10(13) - 10(17) m(-3) s(-1) using an expansion wave tube. The rates agree well with the results of Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)] in the range of overlap (220-240 K), and are summarized by the empirical fit J = S exp[4.6 + 0.244T-(906.8 - 2.914T)(ln S)(2)], with J the nucleation rate in m(-3) s(-1), S the supersaturation, and T the temperature in K. We find that the supersaturation dependence of both our rates and those of Wolk and Strey is lower than classical theory predicts, and that the critical cluster is smaller than the classical critical size. These deviations are explained in the framework of the Tolman theory for surface tension, and the "Tolman length" is estimated from our experimental results. We find a positive Tolman length that increases with decreasing temperature, from about 0.1 Angstrom at 260 K to (0.6 +/- 0.4) Angstroms at 200 K. We present a nucleation rate expression that takes the Tolman length into account and show that both the supersaturation and temperature dependence are improved, compared to the classical theory.     

Drop in a metastable vapor: Laplace equation,surface tension,and minimum drop size

A van der Waals mean field theory is applied to a Lennard–Jones fluid for studying drop formation in a supersaturated vapor. A spherical surface separates the fluid particles in two homogeneous regions. The model provides densities, radii, minimum radii and excess pressure. By comparing the excess pressure with that given by the Laplace equation, surface tension is worked out. Its dependence on drop size, densities, and temperature, and its asymptotic values to planar interface are found. The model reveals the existence of an absolute minimum drop and drops with densities close to the supersaturated vapor.     

Graphene nucleation on transition metal surface: structure transformation and role of the metal step edge

The nucleation of graphene on a transition metal surface, either on a terrace or near a step edge, is systematically explored using density functional theory calculations and applying the two-dimensional (2D) crystal nucleation theory. Careful optimization of the supported carbon clusters, C(N) (with size N ranging from 1 to 24), on the Ni(111) surface indicates a ground state structure transformation from a one-dimensional C chain to a 2D sp(2) C network at N ≈ 10-12. Furthermore, the crucial parameters controlling graphene growth on the metal surface, nucleation barrier, nucleus size, and nucleation rate on a terrace or near a step edge are calculated. In agreement with numerous experimental observations, our analysis shows that graphene nucleation near a metal step edge is superior to that on a terrace. On the basis of our analysis, we propose the use of graphene seeds to synthesize high-quality graphene in large area.     

Quasihomogeneous nucleation of amyloid beta yields numerical bounds for the critical radius, the surface tension, and the free energy barrier for nucleus formation

Amyloid aggregates are believed to grow through a nucleation mediated pathway, but important aggregation parameters, such as the nucleation radius, the surface tension of the aggregate, and the free energy barrier toward aggregation, have remained difficult to measure. Homogeneous nucleation theory, if applicable, can directly relate these parameters to measurable quantities. We employ fluorescence correlation spectroscopy to measure the particle size distribution in an aggregating solution of Alzheimer's amyloid beta molecule (Abeta(1-40)) and analyze the data from a homogeneous nucleation theory perspective. We observe a reproducible saturation concentration and a critical dependence of various aspects of the aggregation process on this saturation concentration, which supports the applicability of the nucleation theory to Abeta aggregation. The measured size distributions show a valley between two peaks ranging from 5 to 50 nm, which defines a boundary for the value of the nucleation radius. By carefully controlling the conditions to inhibit heterogeneous nucleation, we can hold off nucleation in a 25 times supersaturated solution for at least up to 3 h at room temperature. This quasi-homogeneous kinetics implies that at room temperature, the surface energy of the Abeta/water interface is > or =4.8 mJ/m(2), the free energy barrier to nucleation (at 25 times supersaturation) is > or =1.93x10(-19) J, and the number of monomers in the nucleus is > or =29.     

Secondary organic aerosol formation from limonene ozonolysis: homogeneous and heterogeneous influences as a function of NO(x)

Limonene has a high emission rate both from biogenic sources and from household solvents. Here we examine the limonene + ozone reaction as a source for secondary organic aerosol (SOA). Our data show that limonene has very high potential to form SOA and that NO(x) levels, O(3) levels, and UV radiation all influence SOA formation. High SOA formation is observed under conditions where both double bonds in limonene are oxidized, but those conditions depend strongly on NO(x). At low NO(x), heterogeneous oxidation of the terminal double bond follows the initial limonene ozonolysis (at the endocyclic double bond) almost immediately, making the initial reaction rate limiting. This requires a high uptake coefficient between ozone and the first-generation, unsaturated organic particles. However, at high NO(x), this heterogeneous processing is inhibited and gas-phase oxidation of the terminal double bond dominates. Although this chemistry is slower, it also yields products with low volatility. UV light suppresses production of the lowest volatility products, as we have shown in earlier studies of the alpha-pinene + ozone reaction.     

Properties of alkali metal atoms deposited on a MgO surface: a systematic experimental and theoretical study

The adsorption of small amounts of alkali metal atoms (Li, Na, K, Rb, and Cs) on the surface of MgO powders and thin films has been studied by means of EPR spectroscopy and DFT calculations. From a comparison of the measured and computed g values and hyperfine coupling constants (hfccs), a tentative assignment of the preferred adsorption sites is proposed. All atoms bind preferentially to surface oxide anions, but the location of these anions differs as a function of the deposition temperature and alkali metal. Lithium forms relatively strong bonds with MgO and can be stabilized at low temperatures on terrace sites. Potassium interacts very weakly with MgO and is stabilized only at specific sites, such as at reverse corners where it can interact simultaneously with three surface oxygen atoms (rubidium and cesium presumably behave in the same way). Sodium forms bonds of intermediate strength and could, in principle, populate more than a single site when deposited at room temperature. In all cases, large deviations of the hfccs from the gas-phase values are observed. These reductions in the hfccs are due to polarization effects and are not connected to ionization of the alkali metal, which would lead to the formation of an adsorbed cation and a trapped electron. In this respect, hydrogen atoms behave completely differently. Under similar conditions, they form (H(+))(e(-)) pairs. The reasons for this different behavior are discussed.     

Evaporation dynamics of a binary sessile droplet: Theory and comparison with experimental data on a droplet of a sulfuric-acid solution

Diffusion evaporation of a sessile binary droplet in an atmosphere of a noncondensable carrier gas has been considered. For a droplet consisting of two infinitely miscible liquids, a relation between the current values of solution concentration and volume of the droplet has been derived in an explicit form under the ideal solution approximation. It has been shown that the volume of a sessile binary droplet may, as well as the volume of a free binary droplet, vary nonmonotonically with time. The evaporation of a droplet of an aqueous sulfuric-acid solution has been considered in detail taking into account the nonideality of the solution. Time variations in the volume, base area, and contact angle have been experimentally measured for the sessile droplet of an aqueous sulfuric-acid solution on a hydrophobized substrate. The experimental data obtained at different initial humidities of water-vapor and droplet-solution concentrations have been analyzed within the theory of the stationary isothermal diffusion evaporation of a sessile binary droplet.     

PVC miniemulsion polymerization II. Particle and droplet growth as a function of conversion

Growth of two droplet families and a polymer seed family as a function of percent monomer conversion in PVC miniemulsion synthesis demonstrates that polymerization in droplets predominates to ～ 30–40% conversion, whereupon polymerization of seed becomes favored. This difference appears to be due to a liquid-to-solid phase change in the forming particles during the course of polymerization.     

Escape from a cavity through a small window: turnover of the rate as a function of friction constant

To escape from a cavity through a small window the particle has to overcome a high entropy barrier to find the exit. As a consequence, its survival probability in the cavity decays as a single exponential and is characterized by the only parameter, the rate constant. We use simulations to study escape of Langevin particles from a cubic cavity through a small round window in the center of one of the cavity walls with the goal of analyzing the friction dependence of the escape rate. We find that the rate constant shows the turnover behavior as a function of the friction constant, zeta: The rate constant grows at very small zeta, reaches a maximum value which is given by the transition-state theory (TST), and then decreases approaching zero as zeta-->infinity. Based on the results found in simulations and some general arguments we suggest a formula for the rate constant that predicts a turnover of the escape rate for ergodic cavities in which collisions of the particle with the cavity walls are defocusing. At intermediate-to-high friction the formula describes transition between two known results for the rate constant: the TST estimation and the high friction limiting behavior that characterizes escape of diffusing particles. In this range of friction the rate constants predicted by the formula are in good agreement with those found in simulations. At very low friction the rate constants found in simulations are noticeably smaller than those predicted by the formula. This happens because the simulations were run in the cubic cavity which is not ergodic.